In [10]:
import os
import sys
import copy
import json
import math
from math import pow, sqrt
import datetime
from datetime import date
import matplotlib
import QuantLib as ql
import multiprocessing
from scipy.optimize import root
import numpy as np
import pandas as pd
from scipy.stats import norm
from importlib import reload
import QuantLib as ql
import itertools
from itertools import groupby, chain, product
from collections import defaultdict
import plotly.figure_factory as ff
from pprint import pprint
import plotly.graph_objs as go
from plotly.subplots import make_subplots
from functools import partial
sys.path.append('..')
import connector.quantconnect.client as mClient
reload(mClient)
import connector.quantconnect.volatility.implied as mOption
reload(mOption)
import research.plotting as mPlot
reload(mPlot)
import connector.quantconnect.helper as h
reload(h)
load = h.load
plot_surface = h.plot_surface
plot_vol_surface = h.plot_vol_surface
import connector.quantconnect.model_calibration as mc
reload(mc)
mp_calibrate_heston = mc.mp_calibrate_heston
CalibrationParams = mc.CalibrationParams
HestonParams = mc.HestonParams
HestonCalibrationResult = mc.HestonCalibrationResult
VolSurfaceData = mc.VolSurfaceData
vega_bsm = mc.vega_bsm
vol_surface_data2vega_surface_data = mc.vol_surface_data2vega_surface_data
bw_silverman = mc.bw_silverman
SurfaceFrameData = mc.SurfaceFrameData
from connector.quantconnect.typess import option_contract
reload(option_contract)
OptionContract = option_contract.OptionContract
from connector.quantconnect.typess.enums import TickType, CsvHeader, Resolution, SecurityType
from connector.quantconnect.typess.option_contract import OptionContract
from connector.quantconnect.typess.equity import Equity
# add plot packages
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D
Config¶
In [6]:
start = datetime.date(2023, 9, 1)
end = datetime.date(2024, 1, 18)
client = mClient.Client()
sym = 'dell'
equity = Equity(sym)
option_right = 'call'
min_dte = 14
f_min_strike = 0.9
f_max_strike = 1.1
bounds = [(0,1), (0.01,25), (0.01,15.), (-1,1), (0,1.0)]
initialHestonParams = HestonParams(0.005, 0.8, 0.008, 0.2, 0.1)
rate = 0.05
dividend_yield = 0.013
Price data load¶
Loading underlying prices¶
In [3]:
trades = client.history([equity], start, end, Resolution.hour, TickType.trade, SecurityType.equity)
ps_spot = trades[sym]['close']
# removing non-RTH hours from spot because not present in quotes
ps_spot = ps_spot[(ps_spot.index.time >= datetime.time(10, 0)) & (ps_spot.index.time <= datetime.time(15, 0))]
ret = np.log(ps_spot / ps_spot.shift(1))
ps_spot.plot()
Out[3]:
<Axes: xlabel='time'>
Loading option prices¶
In [4]:
contracts = client.central_volatility_contracts(equity, start, end, n=300)
contracts = list(chain(*contracts.values()))
print(len(contracts))
3142
In [5]:
quotes = client.history(contracts, start, end, Resolution.hour, TickType.quote, SecurityType.option)
quotes = {OptionContract.from_contract_nm(k): v for k, v in quotes.items()}
Missing dell_quote_american_call_420000_20230901.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_680000_20230901.csv in dell_2024_quote_american.zip Missing dell_quote_american_put_700000_20230901.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_600000_20230901.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_700000_20230901.csv in dell_2024_quote_american.zip Missing dell_quote_american_put_530000_20230901.csv in dell_2024_quote_american.zip Missing dell_quote_american_put_580000_20230901.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_610000_20230901.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_580000_20230901.csv in dell_2024_quote_american.zip Missing dell_quote_american_put_620000_20230901.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_500000_20230901.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_720000_20230901.csv in 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dell_2024_quote_american.zip Missing dell_quote_american_put_900000_20231013.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_745000_20231013.csv in dell_2024_quote_american.zip Missing dell_quote_american_put_1000000_20231013.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_800000_20231013.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_660000_20231013.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_810000_20231013.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_520000_20231013.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_715000_20231013.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_700000_20231013.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_650000_20231013.csv in dell_2024_quote_american.zip Missing dell_quote_american_call_620000_20231013.csv in dell_2024_quote_american.zip Missing 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In [6]:
ix_quotes = pd.concat([df[~df.index.duplicated()] for df in quotes.values()], axis=1).index
print(len(ix_quotes))
706
Sampling underlying price every <min_diff> return¶
In [7]:
assert len(ps_spot.index.unique()) == len(ps_spot)
In [8]:
min_diff_r = 0.01
loc = []
p0 = None
for ix, p in ps_spot.items():
if p0 is None:
p0 = p
loc.append(ix)
continue
if abs(p/p0 - 1) > min_diff_r:
p0 = p
loc.append(ix)
print(len(loc))
87
Error of Vol surface to reference prices¶
In [9]:
def err_srf(volSurface, K2, T1, iv2):
apc = []
srf_error = []
for strike, expiry, iv in zip(K2, T1, iv2):
err = 100 * (ahVolSurface.blackVol(expiry, strike) / iv - 1)
srf_error.append({'expiry': expiry, 'strike': strike, 'error': err})
apc.append(abs(err))
print(np.mean(apc)); print(np.max(apc))
return np.mean(apc), srf_error
In [10]:
calibration_params = CalibrationParams(
datetime.datetime(2000,1,1),
0,
f_min_strike,
f_max_strike,
option_right,
min_dte,
bounds,
initialHestonParams,
rate,
dividend_yield
)
Load or calibrate heston model parameters and source surfaces¶
In [11]:
%%time
#hestonCalibrationResults = mp_calibrate_heston(loc, quotes, ps_spot, calibration_params)
import pickle
with open(rf'C:\repos\quantconnect\Lean\Launcher\bin\Analytics\hestonCalibrationResults_call_2024-01-24T194122.pickle', 'rb') as f:
hestonCalibrationResults = pickle.load(f)
hestonCalibrationResults = [r for r in hestonCalibrationResults if r]
hestonCalibrationResults = [r for r in hestonCalibrationResults if r.error < 100]
CPU times: total: 31.2 ms Wall time: 54.5 ms
In [12]:
print(f'Average calibration error: {np.average([r.error for r in hestonCalibrationResults])}')
Average calibration error: 4.910863582147465
In [13]:
def get_black_vol_surface(ts, volSurfaceData, interpolation="bicubic"):
calculation_date = ql.Date(ts.day, ts.month, ts.year)
calendar = ql.UnitedStates(ql.UnitedStates.NYSE)
tenorsQlDt = [calendar.advance(calculation_date, ql.Period(int(t * 365), ql.Days)) for t in volSurfaceData.tenors]
day_count: ql.DayCounter = ql.Actual365Fixed()
blackVolSurface = ql.BlackVarianceSurface(calculation_date, calendar, tenorsQlDt, volSurfaceData.strikes, ql.Matrix(volSurfaceData.volatilities.transpose().tolist()), day_count)
blackVolSurface.setInterpolation(interpolation)
return blackVolSurface
In [14]:
ts_vol_surfaces = {r.ts: get_black_vol_surface(r.ts, r.VolSurfaceData) for r in hestonCalibrationResults}
ts_vega_surfaces = {r.ts: vol_surface_data2vega_surface_data(r.VolSurfaceData, r.calibration_params) for r in hestonCalibrationResults}
params_exp = most_probable_heston_params(heston_calibration_results)
ts_model_engines_exp = {r.ts: setup_model(
r.calibration_params.yield_ts, r.calibration_params.dividend_ts, r.calibration_params.spot, init_condition=params_exp.params()
) for r in hestonCalibrationResults}
ts_model_engines_0 = {r.ts: setup_model(
r.calibration_params.yield_ts, r.calibration_params.dividend_ts, r.calibration_params.spot, init_condition=calibration_params.heston_params.params()
) for r in hestonCalibrationResults}
ts_utility_surfaces = {t.ts: None for r in calibration_results}
--------------------------------------------------------------------------- AttributeError Traceback (most recent call last) Cell In[14], line 1 ----> 1 ts_vol_surfaces = {r.ts: get_black_vol_surface(r.ts, r.VolSurfaceData) for r in hestonCalibrationResults} 2 ts_vega_surfaces = {r.ts: vol_surface_data2vega_surface_data(r.VolSurfaceData, r.calibration_params) for r in hestonCalibrationResults} 4 params_exp = most_probable_heston_params(heston_calibration_results) Cell In[14], line 1, in <dictcomp>(.0) ----> 1 ts_vol_surfaces = {r.ts: get_black_vol_surface(r.ts, r.VolSurfaceData) for r in hestonCalibrationResults} 2 ts_vega_surfaces = {r.ts: vol_surface_data2vega_surface_data(r.VolSurfaceData, r.calibration_params) for r in hestonCalibrationResults} 4 params_exp = most_probable_heston_params(heston_calibration_results) AttributeError: 'HestonCalibrationResult' object has no attribute 'VolSurfaceData'
In [6]:
print(f'# hestonCalibrationResults: {len(hestonCalibrationResults)}')
# hestonCalibrationResults: 181
Plot and analyze Heston parameters over time¶
- errors: vs src arb free srf. ok. vs non-arb free srf, missing. save with Heston Calib Results... Ideally with bid/ask prices.
In [21]:
v_v0 = np.array([r.params.v0 for r in hestonCalibrationResults])
v_kappa = np.array([r.params.kappa for r in hestonCalibrationResults])
v_theta = np.array([r.params.theta for r in hestonCalibrationResults])
v_rho = np.array([r.params.rho for r in hestonCalibrationResults])
v_sigma = np.array([r.params.sigma for r in hestonCalibrationResults])
size = 4
v_ts = [r.ts for r in hestonCalibrationResults]
t_v0 = go.Scatter(x=v_ts, y=v_v0, mode='lines+markers', marker=dict(size=size), name='V0')
t_kappa = go.Scatter(x=v_ts, y=v_kappa, mode='lines+markers', marker=dict(size=size), name='Kappa', yaxis='y2')
t_theta = go.Scatter(x=v_ts, y=v_theta, mode='lines+markers', marker=dict(size=size), name='Theta')
t_rho = go.Scatter(x=v_ts, y=v_rho, mode='lines+markers', marker=dict(size=size), name='Rho')
t_sigma = go.Scatter(x=v_ts, y=v_sigma, mode='lines+markers', marker=dict(size=size), name='Sigma', yaxis='y2')
In [17]:
#pd.Series(v_sigma).plot.kde()
In [18]:
for v, label in [(v_v0, 'Variance 0'), (v_kappa, 'Kappa'), (v_theta, 'Theta'), (v_rho, 'Rho'), (v_sigma, 'Vol-Vol')]:
zscore = (v - v.mean()) / v.std()
fig = ff.create_distplot([v], [label], bin_size=(max(v)-min(v))/50)
#fig = ff.create_distplot([zscore], [f'{label} ZScore'], bin_size=0.1, curve_type='kde')
fig.show()
In [19]:
#mPlot.plot_ps_trace(*[go.Scatter(x=v_kappa, y=(v_kappa - v_kappa.mean()) / v_kappa.std(), mode='markers', marker=dict(size=2), name='QQ Kappa')])
In [22]:
traces = [
t_v0,
t_kappa,
t_theta,
t_rho,
t_sigma,
]
mPlot.plot_ps_trace(*traces)
In [23]:
mPlot.plot_ps_trace(*[
go.Scatter(x=v_ts, y=[r.error for r in hestonCalibrationResults], mode='lines+markers', marker=dict(size=size), name='Heston vs AHSrf Mean Abs Pct Error')
])
dIV/dS ->¶
dIV/dK (sticky delta) (neg correlation for OTM. pos for ITM) IV(dS) (expect neg. correlation)
Start with dIV/dK. From repaired, arb-free or heston? Whichever minimized hedging error the most!
- load. pick every x% return. calc practitioner delta, theta. Calc theta contribution.
- dP, dSdelta, dSdeltaMV, err1, err2
Assuming heston param mean reversion. Discover IV trade opps
- Calc most likely param state. KDE. Done
- Subtract (srf0 - surfMean). Conditional upon srf0 heston param perturbed enough. utility...
- add price difference to PL for all hypothetical deals
Using Basin Hoppin Solver¶
In [90]:
In [1240]:
In [336]: